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This is relative depending on your subject. Slow motion for a person walking could be 60fps while a car may be 1000fps. Both of these are examples of the capture rate. They are captured at this rate and then replayed around 30fps.

Determining necessary frame rate: Think of your subject's action that you want to slow down. If it's a drift in a car, lets say it took 1 second for that car to come around the bend. How long would you like it to take in the video? 2 seconds? 60fps. 4 seconds? 120fps. You simply do the math to determine what fps you want to capture.

You'll find that the most popular DSLRs (and helmet cams) are going to capture at 60fps. Usually this won't meet your needs of slow motion. To compensate, many professionals are using a software solution that is much cheaper than a hardware solution. Twixtor is one of the leading models and has been able to slow some videos to the equivalent of 2000fps (remember, playback is always around 30fps) from a 60fps capture. I say "some" because the software is attempting to determine what occurred between the missing frames and this can cause artifacts. If you're shocked by the sticker price of Twixtor, take a moment and research prices of cameras that capture at the rate Twixtor can almost duplicate, at 1080p, without having to carry that price tag around potentially dangerous areas. Then try and strap one of those cameras to your bike/wakeboard/car.

In tecnical terms of Slow Motion, you can record at any speed, the fact is that actually slow motion... is achieved when each film frame is captured at a rate much faster than it will be played back.The technical term for slow motion is overcranking which refers to the concept of cranking a handcranked camera at a faster rate than normal (i.e. faster than 24 frames per second).
A third technique that is becoming common using current computer software post-processing (with programs like Twixtor) is to fabricate digitally interpolated frames to smoothly transition between the frames that were actually shot. Ciberlink PowerDVD uses that interpolation for ex.

Answering your question, you can achieve slow motion with any video recorder, the more frames per second, the better or smoothly... and of course you can use software post-processing to smooth frames out.

To add to this answer, another thing to really consider is what you want to shoot in slow-mo. As @AndyML said below, it's all in planning of what you want to shoot. This is especially true if you're going to Twixtor your footage.
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nchpmnJul 3 '12 at 2:54